while SpaceX has been doing it, approximately 300 times

We’re discussing upper stages here, not first stages. SpaceX have recovered 339 (soon to be 340 in a few hours) first stages, not orbital upper stages.

SpaceX still haven’t technically recovered any orbital upper stages yet, though Starship IFT-4 came very close. They successfully brought the ship back from orbital velocity but a suborbital trajectory.

Blue Origin still have yet to launch anything into orbit.